Optimal manufacturer's replenishment policies for deteriorating items in a supply chain with up-stream and down-stream trade credits

Liao (2008) presented the optimal retailer's replenishment policies in the EPQ model for deteriorating items with two-level trade credit, in which the retailer receives the supplier trade credit M, and provides the customer trade credit N(N < M) simultaneously. In this paper, we extend her EPQ model to complement the shortcoming of her model. In addition, we relax the dispensable assumption of N < M and others. We then establish an appropriate EPQ model to the problem. Next, we propose a simple arithmetic-geometric inequality method to find the optimal solution when the deterioration rate is sufficiently small. We also develop the proper theoretical results to obtain the optimal solution when the deterioration rate is not sufficiently small. Finally, numerical examples are presented to illustrate the proposed model and its optimal solution. (C) 2010 Elsevier B.V. All rights reserved.